Generation of High-Resolution Water Surface Slopes From Multi-Mission Satellite Altimetry

For nearly three decades, satellite radar altimetry has provided measurements of the water surface elevation (WSE) of rivers. These observations can be used to calculate the water surface slope (WSS), which is an essential parameter for estimating flow velocity and river discharge. In this study, we calculate a non time-varying high-resolution WSS of 11 Polish rivers based on multi-mission altimetry observations from 11 satellites in the period from 1994 to 2023. The proposed approach is based on a weighted least squares adjustment with an additional Laplace condition and an a priori gradient condition. The processing is divided into river sections not interrupted by dams and reservoirs. After proper determination of the WSE for each river kilometer (bin), the WSS between adjacent bins is calculated. To assess the accuracy of the estimated WSS, it is compared with slopes between gauge stations, which are referenced to a common vertical datum. Such gauge stations are available for 8 studied rivers. The root mean squared error (RMSE) ranges from 4 mm/km to 77 mm/km, with an average of 27 mm/km. However, the mean RMSE decreases to 11 mm/km when the 2 mountain rivers are excluded. The WSS accuracies are also compared with slope data sets based on digital elevation models, ICESat-2 altimetry, and lidar. For 6 rivers the estimated WSS shows the highest accuracy. The improvement was particularly significant for mountain rivers. The proposed approach allows an accurate, non time-varying high-resolution WSS even for small and medium-sized rivers and can be applied to almost any river worldwide. The Water Surface Slope (WSS) of a river is a measure of how steeply it flows downstream. This value affects the velocity of the water and also the force with which the water erodes the river bed. WSS is calculated by dividing the difference between two water surface elevations (WSE) by the length of the river section between these points. In this paper, we determine the non time-varying WSS on almost every kilometer of 11 Polish rivers. For this purpose, we used almost 30 years of satellite altimetry measurements, which provide information about the height of the water surface at a given place and time. After filtering and mathematical adjustment of these measurements, we determined the WSE and WSS on almost every kilometer of the studied rivers. We compared our results with the average gradients between neighboring water level gauge stations, and for most rivers we obtained very small errors. Compared to other sources of WSS data, our method showed the highest accuracy. The results presented in this work are the first such accurate and spatially dense WSS information of Polish rivers. Moreover, the proposed method allows the determination of WSS on almost any river in the world. High-resolution non time-varying water surface slope (WSS) for 11 Polish rivers have been determined using cross-calibrated multi-mission altimetry measurements For 8 rivers studied, we obtained a mean root mean square error of 27 mm/km, which decreases to 11 mm/km if 2 mountain rivers are excluded For 6 rivers, the estimated WSS showed the highest accuracy compared to WSS data sets based on digital elevation models, ICESat-2, or lidar